## Accidental eccentricity

When the distributions of stiffness and/or mass in plan are unsymmetric, the response to the horizontal components of the seismic action has certain torsional-translational features. These features are sufficiently taken into account in an analysis in 3D for the horizontal components, especially when a modal response spectrum analysis or a non-linear dynamic one is performed. Unlike some other seismic design codes, amplification or de-amplification of the 'natural' eccentricities between the centres of mass and stiffness is not required. This is convenient, because normally the storey stiffness centre cannot be uniquely defined (see Section 4.3.2.1). Moreover, determination of the position of a conventionally defined

Clauses 4.3.2(1), 4.3.3.2.4(2), 4.3.6.3.1(2), 4.3.6.3.1(4)

storey stiffness centre at a level of accuracy and sophistication consistent with the dynamic amplification of natural eccentricities, requires tedious additional analyses.

For buildings with full symmetry of stiffness and nominal masses in plan, the analysis for the horizontal components of the seismic action gives no torsional response at all. Effects which cannot be captured by conventional seismic response analysis according to Eurocode 8, such as variations in the stiffness and mass distributions from the nominal ones considered in the analysis, or a possible torsional component of the ground motion about a vertical axis, may produce a torsional response even in nominally fully symmetric buildings. To ensure a minimum of torsional resistance and stiffness and limit the consequences of unforeseen torsional response, EN 1998-1 introduces accidental torsional effects by displacing the masses with respect to their nominal positions adopted in modelling. This displacement is assumed to take place in the positive and in the negative sense along any horizontal direction (in practice, along the two orthogonal directions of the horizontal seismic action components). It is more conservative for the global seismic action effects to consider that all the masses of the structure are displaced along the same horizontal direction and in the same sense (positive or negative) at a time.

It is completely impractical to study the effect of displacing the masses through dynamic analysis: the dynamic characteristics of the system will change with the location of the masses. So, Eurocode 8 allows replacing the 'accidental eccentricity' of the masses from their nominal positions, by 'accidental eccentricity' of the horizontal seismic components with respect to the nominal position of the masses. All accidental eccentricities are considered at a time along the same horizontal direction and in the same sense (positive or negative). The effects of this accidental eccentricity are determined through static approaches.

The accidental eccentricity of a horizontal seismic action component is specified as a fraction of the dimension of the storey in plan orthogonal to this horizontal component. The fraction of the storey plan dimension is normally 5%; it is doubled to 10% if the effects of accidental eccentricity are taken into account in the simplified way described in Section 4.8.3 and, in addition, instead of a full structural model in 3D for each horizontal component of the seismic action, a separate 2D model is analysed (which is allowed in structures regular in plan, but entails neglecting any small static eccentricity that may exist between the floor centres of stiffness and mass). Moreover, if there are masonry infills with a moderately irregular and unsymmetric distribution in plan (this excludes strongly irregular arrangements, such as infills mainly along two adjacent faces of the building), the effects of the accidental eccentricity are doubled further (i.e. as if the accidental eccentricity is 10% of the orthogonal dimension of the storey in the reference case, or 20% for simplified evaluation of accidental torsional effects when using two separate 2D models).

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### Responses

• callan
What is accidental eccentricity?
2 years ago